To compare the phase behavior of linear and hyperbranched polymers, the phase envelopes of the ternary system linear polyglycerol + methanol + carbon dioxide were determined for polymers of varying molar mass. Phase changes were detected by a static synthetic method using the Cailletet setup for temperatures between 331 K and 421 K and pressures up to 13.1 MPa. Besides the vapor-liquid and liquid-liquid equilibria, also the vapor-liquid to vapor-liquid-liquid and vapor-liquid-liquid to liquid liquid phase boundaries are reported. The experimental results are similar to systems with hyperbranched polymers (rather than linear polymers). For the systems with linear polymers, however, the bubble-point pressures show no significant dependence on the polymer molar mass, whereas for hyperbranched polymers the bubble-point pressure was found to vary substantially with the polymer molecular mass. Further, the polymer concentration at the lower critical solution temperature is remarkably high when the polymers have a hyperbranched structure (Schacht et al., Fluid Phase Equilib. 2010, 299, 252-258), while the polymer concentration is much lower for systems with linear polymers.